The definition of a straight line according to google.
I do not understand why I call these geometries "non-Euclidean". In my view, both hyperbolic and elliptical geometry are just a dimensional reference change of the plane, using the same elements described by Euclid. Both are described by curved planes, that is, analyzed three-dimensionaly. A straight line is no longer a straight line. Perhaps there is a lost axiom that has not been introduced to better define what a line is and not to confuse it with a curve. What I want to mean is that, all of these are the same elements but with another perspective. If we can define what a line really is, maybe we can debunk the axioms denying the parallels axiom. If anyone has understood my doubt, please tell me where I am wrong or if there is truth in my words. Thanks.